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Multiscale Green's function
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<p>Multiscale Green's function (MSGF) is a generalized and extended version of the classical <a href="/facts/Green%2527s_function/rKxKKPcp">Green's function</a> (GF) technique for solving mathematical equations. The main application of the MSGF technique is in modeling of <a href="/facts/Nanomaterials/BthrFILJ">nanomaterials</a>. These materials are very small – of the size of few <a href="/facts/Nanometer/a98sjHyu">nanometers</a>. Mathematical modeling of nanomaterials requires special techniques and is now recognized to be an independent branch of science. A mathematical model is needed to calculate the displacements of atoms in a crystal in response to an applied static or time dependent force in order to study the mechanical and physical properties of nanomaterials. One specific requirement of a model for nanomaterials is that the model needs to be multiscale and provide seamless linking of different length scales. </p><p><a href="/facts/Green%2527s_function/rKxKKPcp">Green's function</a> (GF) was originally formulated by the British mathematical physicist <a href="/facts/George_Green_(mathematician)/89DMr6wz">George Green</a> in the year 1828 as a general technique for solution of operator equations. It has been extensively used in mathematical <a href="/facts/Physics/a7aH2y08">physics</a> over the last almost two hundred years and applied to a variety of fields. Reviews of some applications of GFs such as for <a href="/facts/Green%2527s_function_(many-body_theory)/1v3ethbc">many body theory</a> and <a href="/facts/Green%2527s_function_for_the_three-variable_Laplace_equation/K21gGXLc">Laplace equation</a> are available in the Wikipedia. The GF based techniques are used for modeling of various physical processes in materials such as <a href="/facts/Phonon/tflWW6vw">phonons</a>, <a href="/facts/Electronic_band_structure/W5o7oE2R">Electronic band structure</a> and <a href="/facts/Elastostatics/wcJoIFg1">elastostatics</a>. </p>